Correlation, as the name suggests, gives the measure of the relationship between two variables.
In statistical terms, it is the measure using which statisticians figure out how much two things are related.
Two things could be related in different extend and ways. For eg:
1) If one variable increases, the other variable might increase(+ve correlation), decreases(-ve correlation) or remain unchanged/have no defined pattern( uncorrelated ).
2) Also, this behavior could remain the same for all the values(monotonic) or can vary with the values.